A series LCR circuit having $\mathrm{R}=44 \Omega, \mathrm{~L}=2 \mathrm{H}$ and $\mathrm{C}=25 \mu \mathrm{~F}$ is connected to a variable frequency of 220 V . What is the average power transferred to the circuit in one complete cycle if the frequency of supply equals the natural frequency of the circuit?

In a pure inductive circuit, a sinusoidal voltage $V(t)=200 \sin 250 t$ is applied to a pure inductance of $\mathrm{L}=0.02 \mathrm{H}$. The current through the coil is:

The instantaneous values of alternating current and voltages in a circuit are $\mathrm{I}=\frac{3}{\sqrt{2}} \sin (200 \pi t)$ ampere and $\mathrm{V}=\frac{3}{\sqrt{2}} \sin \left(200 \pi t+\frac{\pi}{6}\right)$ volt. What is the average power consumed in the circuit in watt ?

The ratio of the number of turns of the primary coil to the secondary coil of an ideal transformer is $5: 1$. The primary is connected to 220 V supply. What is the output power of the transformer if the output resistance is $11 \Omega$ ?